Formation and maintenance of nitrogen-fixing cell patterns in filamentous cyanobacteria

Cyanobacteria forming one-dimensional filaments are paradigmaticmodel organisms of the transition between unicellular andmulticellular living forms. Under nitrogen-limiting conditions, infilaments of the genus Anabaena, some cells differentiate into heterocysts,which lose the possibility to divide but are able to fixenvironmental nitrogen for the colony. These heterocysts form aquasiregular pattern in the filament, representing a prototype ofpatterning and morphogenesis in prokaryotes. Recent years haveseen advances in the identification of the molecular mechanism regulatingthis pattern. We use these data to build a theory on heterocystpattern formation, for which both genetic regulation and theeffects of cell division and filament growth are key components. Thetheory is based on the interplay of three generic mechanisms: localautoactivation, early long-range inhibition, and late long-range inhibition.These mechanisms can be identified with the dynamics ofhetR, patS, and hetN expression. Our theory reproduces quantitativelythe experimental dynamics of pattern formation and maintenancefor wild type and mutants. We find that hetN alone is notenough to play the role as the late inhibitory mechanism: a secondmechanism, hypothetically the products of nitrogen fixation suppliedby heterocysts, must also play a role in late long-range inhibition.The preponderance of even intervals between heterocysts arisesnaturally as a result of the interplay between the timescales of geneticregulation and cell division.We also find that a purely stochasticinitiation of the pattern, without a two-stage process, is enoughto reproduce experimental observations.Funding from the Spanish Ministry of Economy and Competitiveness through Grant PHYSDEV (FIS2012-32349) and the Ramón y Cajal Program (to S.A.)

Modelos de superficies e intercaras : transiciones de fase, desorden y aplicaciones

En esta memoria estudiamos varios modelos formulados en una dimensión. Primero estudiamos el modelo de sine-Gordon, que es adecuado para estudiar el crecimiento de superficies sólidas, encontrando un comportamiento de tamaño finito semejante a una transición de fase termodinámica. A continuación hemos presentado dos modelos de la transición de mojado de superficies. Hemos utilizado la versión con desorden de estos modelos para caracterizar la dependencia con la secuencia genética de la temperatura de desnaturalización del ADN. Combinando uno de los modelos de mojado con el de sine-Gordon proponemos un modelo nuevo, cuya versión con desorden nos permite hacer comparaciones con el modelo de sine-Gordon en dos dimensiones. De ello hacemos la conjetura que la fase superrugosa del modelo en dos dimensiones es en realidad una fase plana dominada por el desorden. A continuación, utilizando el modelo de Dauxois-Peyrard-Bishop, estudiamos el efecto de las burbujas de desnaturalización en el ADN. Nuestros resultados coinciden con los experimentales, de lo cual deducimos importantes consecuencias sobre la dinámica de burbujas. Finalmente, proponemos un modelo nuevo para el estudio de la dinámica de horquillas de ADN que nos permite poner a prueba las interpretaciones vigentes sobre los resultados experimentales

Optimal cellular mobility for synchronization arising from the gradual recovery of intercellular interactions

Cell movement and intercellular signaling occur simultaneously during the development of tissues, but little is known about how movement affects signaling. Previous theoretical studies have shown that faster moving cells favor synchronization across a population of locally coupled genetic oscillators. An important assumption in these studies is that cells can immediately interact with their new neighbors after arriving at a new location. However, intercellular interactions in cellular systems may need some time to become fully established. How movement affects synchronization in this situation has not been examined. Here we develop a coupled phase oscillator model in which we consider cell movement and the gradual recovery of intercellular coupling experienced by a cell after movement, characterized by a moving rate and a coupling recovery rate respectively. We find (1) an optimal moving rate for synchronization, and (2) a critical moving rate above which achieving synchronization is not possible. These results indicate that the extent to which movement enhances synchrony is limited by a gradual recovery of coupling. These findings suggest that the ratio of time scales of movement and signaling recovery is critical for information transfer between moving cells.Comment: 18 single column pages + 1 table + 5 figures + Supporting Informatio

Modelling of patA and hetF gene function in Anabaena heterocyst formation

[Póster presentado a]: XXII Congreso de Física Estadística (FisEs'18), Madrid, 18-20 de octubre de 2018.Differentiated cell types can form patterns in filamentous cyanobacteria. Specifically the genus Anabaena has received special interest because under nitrogen-limiting conditions some of the vegetative cells differentiate into a nitrogen-fixing form called heterocyst [1]. These heterocysts cannot undergo cell division or have photosynthetic activity, but share fixed nitrogen products with the whole filament. In order to efficiently distribute the fixed nitrogen, heterocysts are arranged forming quasiregular patterns in the filament..

Predictability: Can the turning point and end of an expanding epidemic be precisely forecast?

No, they can't. Epidemic spread is characterized by exponentially growing dynamics, which are intrinsically unpredictable. The time at which the growth in the number of infected individuals halts and starts decreasing cannot be calculated with certainty before the turning point is actually attained; neither can the end of the epidemic after the turning point. An SIR model with confinement (SCIR) illustrates how lockdown measures inhibit infection spread only above a threshold that we calculate. The existence of that threshold has major effects in predictability: A Bayesian fit to the COVID-19 pandemic in Spain shows that a slow-down in the number of newly infected individuals during the expansion phase allows to infer neither the precise position of the maximum nor whether the measures taken will bring the propagation to the inhibition regime. There is a short horizon for reliable prediction, followed by a dispersion of the possible trajectories that grows extremely fast. The impossibility to predict in the mid-term is not due to wrong or incomplete data, since it persists in error-free, synthetically produced data sets, and does not necessarily improve by using larger data sets. Our study warns against precise forecasts of the evolution of epidemics based on mean-field, effective or phenomenological models, and supports that only probabilities of different outcomes can be confidently given.Comment: 13 pages, 4 figure + Supplementary Informatio

Synchronization Dynamics in the Presence of Coupling Delays and Phase Shifts

In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be regulated by substituting time delays by phase shifts at a constant collective frequency. For spatially extended systems with time delays, we show that the fastest synchronization can occur for intermediate wavelengths, giving rise to novel synchronization scenarios.This work was supported by spanish Ministry of Economy and Competitiveness (MINECO) through Grant PHYSDEV (No. FIS2012-32349) and from CSIC through the Junta para la Ampliación de Estudios program (JAEDOC014, 2010 call) cofunded by the European Social FundPublicad

Nitrogen-fixing cyanobacteria are tuned for evolvability

Cyanobacteria produce a significant fraction of the oxygen on the environment and, together with archaea, they fix atmospheric nitrogen used by all other organisms. One of the first forms of multicellular organisms on Earth are filamentous cyanobacteria, which constitutCyanobacteria produce a significant fraction of the oxygen on the environment and, together with archaea, they fix atmospheric nitrogen used by all other organisms. One of the first forms of multicellular organisms on Earth are filamentous cyanobacteria, which constitute a paradigmatic model organism of the transition between unicellular and multicellular living forms. The genus Anabaena forms colonies with cells arranged in one-dimensional filaments; under nitrogen-limiting conditions some cells can differentiate into a nitrogen-fixing heterocysts, forming regular patterns to effectively provide nitrogen for the colony. e a paradigmatic model organism of the transition between unicellular and multicellular living forms. The genus Anabaena forms colonies with cells arranged in one-dimensional filaments; under nitrogen-limiting conditions some cells can differentiate into a nitrogen-fixing heterocysts, forming regular patterns to effectively provide nitrogen for the colony..

Delayed coupling theory of vertebrate segmentation

Rhythmic and sequential subdivision of the elongating vertebrate embryonic body axis into morphological somites is controlled by an oscillating multicellular genetic network termed the segmentation clock. This clock operates in the presomitic mesoderm (PSM), generating dynamic stripe patterns of oscillatory gene-expression across the field of PSM cells. How these spatial patterns, the clock's collective period, and the underlying cellular-level interactions are related is not understood. A theory encompassing temporal and spatial domains of local and collective aspects of the system is essential to tackle these questions. Our delayed coupling theory achieves this by representing the PSM as an array of phase oscillators, combining four key elements: a frequency profile of oscillators slowing across the PSM; coupling between neighboring oscillators; delay in coupling; and a moving boundary describing embryonic axis elongation. This theory predicts that the segmentation clock's collective period depends on delayed coupling. We derive an expression for pattern wavelength across the PSM and show how this can be used to fit dynamic wildtype gene-expression patterns, revealing the quantitative values of parameters controlling spatial and temporal organization of the oscillators in the system. Our theory can be used to analyze experimental perturbations, thereby identifying roles of genes involved in segmentation.Comment: published online 10 December 2008, Adv. Online Pub. HFSP Journal (free access

Collective modes of coupled phase oscillators with delayed coupling

We study the effects of delayed coupling on timing and pattern formation in spatially extended systems of dynamic oscillators. Starting from a discrete lattice of coupled oscillators, we derive a generic continuum theory for collective modes of long wavelength. We use this approach to study spatial phase profiles of cellular oscillators in the segmentation clock, a dynamic patterning system of vertebrate embryos. Collective wave patterns result from the interplay of coupling delays and moving boundary conditions. We show that the phase profiles of collective modes depend on coupling delays.Comment: 5 pages, 2 figure